High power microwave transistors find application in power amplifiers (PAs) and other circuit applications. Microwave field effect transistors include aluminum gallium nitride/gallium nitride heterojunction field effect transistors (AlGaN/GaN HFET's), gallium arsenide pseudomorphic high electron mobility transistors (GaAs pHEMT's), gallium arsenide metal-semiconductor field effect transistors (GaAs MESFET's), and silicon laterally diffused metal-oxide semiconductor (Si-LDMOS) transistors. Field effect transistors used in microwave power amplifiers generate heat when non-zero voltage and current simultaneously appear on the drains of amplifier final stage transistors. Therefore, the transistors must be able to efficiently dissipate heat that is generated during operation. In addition, the heat generated by the circuitry increases the temperature of the heat sink used to dissipate heat generated by the transistors. For example, a 100 watt (W) final stage transistor that has a thermal resistance, RJC, of 1.5 degrees Celsius per watt (° C./W) dissipating 100 W of average power, while operating with a heat sink temperature of 100° C., would reach a maximum junction temperature of 250° C. Such a junction temperature may exceed the temperature rating of the device channel and present device reliability problems. Therefore, transistors lower values of RJC are desired. More specifically, designers desire structures and methods that reduce the thermal resistance of such devices.